text:
\section{Introduction}\label{intro}

Studies of \PZ boson production in association with heavy-flavor (HF) jets from the hadronization of heavy (\cPqc or \cPqb) quarks provide important tests of perturbative quantum chromodynamics (pQCD) calculations. A good description of these processes is also important since they form a major background for a variety of physics processes including Higgs boson production in association with a \PZ boson, $\PZ\PH$ ($\PH\to\cPqc\cPaqc$ or $\PH\to\cPqb\cPaqb$), and searches for new physics signatures in final states with leptons and HF jets. Two different approaches are currently available for calculating the \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace production: the five-flavor scheme (5FS)~\cite{Campbell:2003dd} and the four-flavor scheme (4FS)~\cite{Cordero:2009kv}. Both approaches yield consistent results within theoretical uncertainties~\cite{Maltoni}.

Several \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace measurements have been performed by the CDF and D0 Collaborations at the FNAL Tevatron~\cite{CDF,D02,D03} and by the ATLAS, CMS, and LHCb Collaborations at the CERN LHC~\cite{ATLAS,CMS1,LHCb1,LHCb2}.
The D0 Collaboration reported on the first $\sigma(\zcs)/\sigma(\zbs)$ cross section ratio measurement \cite{D02} and observed a significantly higher value compared to next-to-leading order (NLO) pQCD calculations. A measurement of the $\sigma(\zcs)/\sigma(\zbs)$ cross section ratio in 8\TeV proton-proton ($\Pp\Pp$) collisions at the LHC has been recently reported by the CMS Collaboration~\cite{ZCciemat} and is in agreement with predictions from leading order (LO) and NLO calculations obtained with the \MADGRAPH~\cite{Alwall:2011uj} and \MGvATNLO~\cite{mg5} programs, respectively.

The current paper reports on simultaneous measurements of the \cPqc and \cPqb quark jet contents in a sample containing a \PZ boson (in the following, \PZ is used as a shorthand for \PZ/$\gamma^*$) produced in association with at least one jet. These measurements provide the first results for proton-proton collisions at $\sqrt s=13$\TeV. The experimental precision is improved with respect to previous LHC results because of the increased size of the data sample and advanced heavy-flavor tagging techniques. The \PZ bosons are identified through reconstructed dielectrons or dimuons, where the individual leptons are subject to requirements on transverse momentum ($\pt > 25\GeV$) and pseudorapidity ($\abs{\eta} < 2.4$). The dilepton invariant mass must be within a \PZ boson window of 71--111\GeV, and jets are required to have $\pt > 30\GeV$ and $\abs{\eta} < 2.4$.

The following cross section ratios are measured: $\sigma(\zcs)/\sigma(\zj)$, $\sigma(\zbs)/\sigma(\zj)$, and $\sigma(\zcs)/\sigma(\zbs)$. These cross section ratios are measured inclusively and differentially as functions of the transverse momentum of the jet and the \PZ boson, and are unfolded to the particle level taking into account detector effects.
The measurements of the cross section ratios benefit from cancellations of several systematic uncertainties related to the jet, lepton, and luminosity measurements. A number of theory-related uncertainties are reduced as well, including those linked to the details of parton showering and hadronization. Therefore, by measuring cross section ratios one can more precisely compare data with theoretical calculations.

The paper is organized as follows. The CMS experiment and data together with simulated samples used in the analysis are described in Sections~\ref{sec:dec} and~\ref{sec:sample}. Details of the measurements are described in Sections~\ref{sec:sel},~\ref{sec:measurement}, and~\ref{sec:unfolding}, while Sections~\ref{sec:syst} and~\ref{sec:result} present the systematic uncertainties and the measurement results, respectively, followed by a summary in Section~\ref{sec:sum}.

\section{The CMS detector}\label{sec:dec}

The central feature of the CMS apparatus is a superconducting solenoid of 6\unit{m} internal diameter, providing a magnetic field of 3.8\unit{T}. Within the solenoid volume are a silicon pixel and strip tracker, covering a pseudorapidity region of $\abs{\eta}<2.5$, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Forward calorimeters, made of steel and quartz fibers, extend the pseudorapidity coverage provided by the barrel and endcap detectors to $\abs{\eta}<5$. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid and covering $\abs{\eta}<2.4$.

Events of interest are selected using a two-tiered trigger system~\cite{Khachatryan:2016bia}. The first level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100\unit{kHz} within a time interval of less than 4\mus. The second level, known as the high-level trigger, consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around 1\unit{kHz} before data storage.

A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref.~\cite{Chatrchyan:2008zzk}.

\section{Data and simulated samples}\label{sec:sample}

The cross section ratio measurements are based on proton-proton ($\Pp\Pp$) collision data at $\sqrt{s}=13\TeV$ collected with the CMS detector in 2016 and corresponding to an integrated luminosity of 35.9\fbinv~\cite{lumi}. Recorded events have an average 23 additional $\Pp\Pp$ interactions per bunch crossing (pileup) together with the hard process.

Various Monte Carlo (MC) event generators are used to simulate the \zj signal and background processes. The full detector simulation is based on the \GEANTfour package~\citep{geant4}. The simulation includes the pileup effects from the same or nearby bunch crossings by overlapping the hard process of interest with the pileup events. The simulated events are reconstructed with the same algorithms as used for the data.

The \zj events are generated by \MGvATNLO v2.2.2~\cite{mg5} (using 5FS; denoted as \textsc{mg}5\_a\textsc{MC}\xspace in the following) at NLO in pQCD with up to two additional partons at the matrix element level, generated for each parton multiplicity and then merged. The \textsc{mg}5\_a\textsc{MC}\xspace matrix element generator is interfaced with \PYTHIA v8.212~\cite{Sjostrand:2014zea}, which simulates the parton shower and hadronization processes, through the FxFx merging scheme~\cite{Frederix:2012ps} at a matching scale of 19\GeV. The predicted numbers of events from \zj production are estimated using a cross section at next-to-next-to-leading order (NNLO) accuracy obtained from \FEWZ v3.1~\cite{Melnikov:2006kv}.

The background events originate from top quark and diboson processes. Top quark-antiquark (\ttbar) production, which forms the dominant background, is generated at NLO by \POWHEG v2.0~\cite{powheg1,powheg2,powheg3,powheg4} and normalized to a cross section calculated by using~\textsc{top++}~v2.0~\cite{top++} at NNLO accuracy including soft-gluon resummation. The diboson ($\PW\PW$, $\PW\PZ$, $\PZ\PZ$) backgrounds are generated by \PYTHIA while \POWHEG and NLO \textsc{mg}5\_a\textsc{MC}\xspace are used to simulate the single top quark processes ($s$-channel, $t$-channel, and $\cPqt\PW$). The \POWHEG generator is also interfaced with \PYTHIA for parton showering and hadronization. The diboson and single top quark predictions are normalized to NNLO~\cite{Grazzini:2017mhc,Kidonakis:2013zqa} cross sections.

The NNPDF 3.0 NLO and LO parton distribution functions (PDF)~\cite{Ball:2014uwa} are used for the NLO and LO calculations, respectively. \PYTHIA uses the NNPDF 2.3 LO PDF set and the CUETP8M1~\cite{Khachatryan:2015pea} or CUETP8M2T4~\cite{CMS-PAS-TOP-16-021} (\ttbar sample) for the underlying event tune.

\section{Object reconstruction and event selection}\label{sec:sel}

The particle-flow (PF) algorithm~\cite{CMS-PRF-14-001} reconstructs and identifies each individual particle in an event, with an optimized combination of information from the various elements of the CMS detector. The neutral particle energy deposits are determined in the calorimeters, whereas charged tracks are measured in the central tracking and muon systems.

The candidate vertex with the largest value of summed physics-object $\pt^2$ is taken to be the primary $\Pp\Pp$ interaction vertex. The physics objects are the jets, clustered using the jet finding algorithm~\cite{Cacciari:2008gp,Cacciari:2011ma} with the tracks assigned to candidate vertices as inputs, and leptons. More details are given in Ref.~\cite{CMS-TDR-15-02}

Electrons are reconstructed using momentum measurements in the tracker combined with the energy deposits in the ECAL~\cite{Khachatryan:2015hwa}. The identification requirements are based on the ECAL shower shape, matching between the electron track and the energy clusters in the ECAL, and observables characterizing the bremsstrahlung along the electron trajectory. Electrons are required to originate from the primary vertex. The electron momentum is estimated by combining the energy measurement in the ECAL with the momentum measurement in the tracker. The momentum resolution for electrons with $\pt \approx 45\GeV$ from $\PZ \to \Pep \Pem$ decays ranges from 1.7 to 4.5\%. The resolution tends to be better in the barrel region than in the endcaps, and it also depends on the bremsstrahlung energy emitted by the electron as it traverses the material in front of the ECAL. The dielectron mass resolution for $\PZ \to \Pep \Pem$ decays when both electrons are in the ECAL barrel is 1.9\%, and is 2.9\% when both electrons are in the endcaps~\cite{Khachatryan:2015hwa}.

Muon candidates are built by combining signals from the tracker and the muon subsystems. The identification criteria are based on the number of measurements in the detectors, the fit quality of the track, and requirements on its association with the primary vertex. Matching muons to tracks measured in the tracker results in a relative transverse momentum resolution, for muons with \pt up to 100\GeV, of 1\% in the barrel and 3\% in the endcaps~\cite{Sirunyan:2018}.

To reduce the misidentification rate, electrons and muons are required to be isolated.  Activity near an electron (muon) is quantified as the sum of transverse momenta of PF candidates within the isolation cone radius of $\Delta R=\sqrt{\smash[b]{(\Delta\eta)^2+(\Delta\phi)^2}}=0.3$~(0.4) around the electron (muon) track, where $\phi$ is the azimuthal angle. After compensating for the energy contribution from pileup in the isolation cone, the resultant sum is required to be less than 25\% of the lepton transverse momentum. The lepton isolation, along with other requirements to select \zj events, strongly suppresses background events with misidentified dileptons such as \wj and QCD multijets.

Based on the PF candidates, jets are reconstructed using the anti-\kt algorithm with a distance parameter of 0.4. Jet momentum is determined as the vector sum of all particle momenta in the jet; based on simulation this is, on average, within 5 to 10\% of the true jet momentum over the entire \pt spectrum and detector acceptance. Pileup interactions can result in more tracks and calorimetric energy depositions, increasing the apparent jet momentum. To mitigate this effect, tracks originating from pileup vertices are discarded and an offset correction is applied to account for remaining contributions~\cite{jetPU1,jetPU2}. Jet energy corrections are derived from simulation studies so that the average measured response of jets becomes identical to that of particle-level jets. In situ measurements of the momentum balance in dijet, photon+jet, $\PZ$+jet, and multijet events are used to determine any residual differences between the jet energy scale (JES) in data and in simulation, and appropriate corrections are applied~\cite{Khachatryan:2016kdb}.  The jet energy resolution (JER) typically amounts to 16\% at 30\GeV and 8\% at 100\GeV. Additional selection criteria are applied to remove jets potentially dominated by instrumental effects or reconstruction failures~\cite{CMS-PAS-JME-16-003}.

For this analysis, the selection for \zj events starts with the trigger requirements based on two electron (muon) objects identified by the trigger system that pass \pt thresholds of 23 and 13\GeV (17 and 8\GeV). The \zj events are further selected by requiring two reconstructed electrons or muons with $\pt > 25\GeV$ and within $\abs{\eta}<2.4$. The \pt requirement is chosen to obtain high trigger efficiency for selecting the signal events. Events containing two selected electrons (muons) are categorized in the electron (muon) channel. The lepton candidates are subject to requirements on their transverse impact parameter, $\abs{d_{xy}} < 0.05\unit{cm}$, and their longitudinal impact parameter, $\abs{d_z} < 0.2\unit{cm}$, both with respect to the primary vertex. The \PZ boson candidate is reconstructed from a pair of oppositely charged same-flavor leptons with invariant mass between 71 and 111\GeV. An event must contain at least one associated jet with $\pt > 30\GeV$ and $\abs{\eta}<2.4$.

Missing transverse momentum is used in this analysis to reduce background contributions from \ttbar and single top quark production processes. In contrast to the \zj, these processes have a significant amount of missing energy because of undetected neutrinos in top quark decays. The missing transverse momentum vector, \ptvecmiss, is computed as the negative vector sum of the transverse momenta of all PF candidates in an event~\cite{CMS-PAS-JME-17-001_paper} and is further modified to account for corrections to the energy scale of the reconstructed jets. Its magnitude, \ptmiss, is required to be less than 40\GeV, which results in a signal efficiency of ${\approx}80\%$ with the \ttbar rejection factor of ${\approx}4.8$.

A \zj sample with enriched \cPqc and \cPqb quark jet content is selected by applying an HF tagging requirement to jets in the \zj sample described above. The discrimination of HF jets from light-flavor quark and gluon jets, referred to as light jets in the following, is achieved by constructing a discriminator variable from tracks and secondary vertex (SV) characteristics. Artificial neural network algorithms are used to combine specific properties of the HF quarks, long lifetime and substantial mass, to build the discriminator. The algorithm used in the analysis, the combined secondary vertex (Version 2), is described in Ref.~\cite{csv}. Some of the important input variables are the number of secondary vertices and the number of tracks associated with each of them, the mass and 2D decay distance significance of the SV with the smallest decay distance uncertainty, and the signed 3D impact parameter significance of the tracks. Here the significance is defined as the ratio between a measured quantity and its uncertainty. Although the combined secondary vertex (Version 2) is trained to distinguish \cPqb~jets\xspace, it does occasionally tag a \cPqc~jet\xspace. Therefore, at a proper operating point, the algorithm can retain a sufficient amount of \cPqc~jets\xspace while heavily suppressing light jets. The analysis uses a ``medium" operating point, which corresponds to approximately 10 (60)\% tagging efficiencies for \cPqc (\cPqb) quark jets and a misidentification probability of 1\% for a light jet. The \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace sample must contain at least one tagged jet. The tagging efficiencies are determined using MC samples and corrected for the difference between data and simulation. The corresponding correction factors are derived from the data versus simulation efficiency comparisons in dedicated control samples containing \ttbar and multijet events~\cite{csv}.

In simulation, the classification of reconstructed \zj events into \zcs, \zbs, and \zls categories is based on the flavors of reconstructed jets with $\pt > 30\GeV$ and $\abs{\eta}<2.4$. They are classified as \cPqc or \cPqb jets if they are matched to MC generated \cPqc or \cPqb hadrons~\cite{csv}. In the case where both \cPqc and \cPqb hadrons are matched, the jet is considered a \cPqb~jet\xspace. Based on reconstructed jets with defined flavors, events are classified as \zbs if they contain at least one \cPqb~jet\xspace. Of the remaining events, those that contain at least one \cPqc hadron are considered as \zcs and those that contain neither \cPqc nor \cPqb hadrons are classified as \zls.

Table~\ref{tab:event_counts} lists the number of events estimated in simulation and found in data that satisfy the \zj and \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace selection criteria for both the electron and muon channels. The background, mostly from top quark and diboson processes, is approximately 5\% in the \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace sample, and the diboson background is dominated by the $\PW\PZ$ events.

\begin{table*}[hbt]
  \topcaption{Numbers of events that satisfy the \zj and \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace selection criteria in the electron and muon channels. The uncertainties are statistical only.}
  \label{tab:event_counts}
  \centering
  \begin{scotch}{lcccc}
   & \multicolumn{2}{c}{\zj sample} & \multicolumn{2}{c}{\ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace sample}\\
   &                     Electron &          Muon &          Electron            & Muon\\
  \hline
  \zcs & 171\,970 $\pm$ 530   & 287\,090 $\pm$ 720  & 18\,870 $\pm$ 170 & \xspace\xspace 32\,310 $\pm$ 230\\
  \zbs & \xspace\xspace 95\,910 $\pm$ 410 & 159\,500 $\pm$ 560   & 60\,100 $\pm$ 310 & 100\,630 $\pm$ 420\\
  \zls &              1\,531\,900 $\pm$ 1\,600 & 2\,612\,100 $\pm$ 2\,200 & \xspace\xspace 6\,170 $\pm$ 100 & \xspace\xspace 10\,810 $\pm$ 140\\
  \ttbar & \xspace\xspace 5\,850 $\pm$ 50      & \xspace \xspace 9\,440 $\pm$ 60 & 3\,850 $\pm$ 40 & \xspace\xspace 6\,180 $\pm$ 50\\
  Diboson & 10\,040 $\pm$ 60      & 16\,310 $\pm$ 80     & \xspace\xspace\xspace 780 $\pm$ 20 & \xspace\xspace 1\,320 $\pm$ 20\\
  Single \cPqt & \xspace\xspace\xspace\xspace\xspace 580 $\pm$ 10       & \xspace\xspace\xspace\xspace\xspace 950 $\pm$ 10 & \xspace 303 $\pm$ 7 & \xspace\xspace\xspace\xspace 500 $\pm$ 10\\
  [\cmsTabSkip]
  Total, simulation &          1\,816\,200 $\pm$ 1\,700 & 3\,085\,400 $\pm$ 2\,400 & 90\,070 $\pm$ 370 & 151\,740 $\pm$ 510\\
  Data &              1\,759\,047            & 2\,959\,629            & 79\,015 &   130\,775 \\
  Data/simulation & \xspace\xspace\xspace\xspace\xspace\xspace\xspace 0.969 $\pm$ 0.001  & \xspace\xspace\xspace\xspace\xspace\xspace\xspace 0.959 $\pm$ 0.001  & \xspace\xspace\xspace\xspace\xspace 0.877 $\pm$ 0.005 & \xspace\xspace\xspace\xspace\xspace\xspace\xspace 0.862 $\pm$ 0.004\\
  \end{scotch}
\end{table*}

\section{Cross section ratio measurements}\label{sec:measurement}
\subsection{Analysis strategy}\label{subsec:strategy}

The goal of the analysis is to precisely measure the fraction of jets with heavy flavors in \zj events. For this purpose, the SV invariant mass, \ensuremath{M_\text{SV}}\xspace, of the tagged jet with highest \pt in the \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace events is used. The SV is reconstructed using an adaptive vertex reconstruction algorithm~\cite{Waltenberger:1166320} from selected tracks within a cone of $\Delta R < 0.3$ around the jet axis. The distance between the track and the jet axis measured at their point of closest approach must be less than 0.2\cm. Details of track selections and SV reconstructions can be found in Refs.~\cite{BTV12001,csv}. The \ensuremath{M_\text{SV}}\xspace is calculated using the momenta of charged-particle tracks associated with the SV. The corresponding particles are assumed to have the pion mass for the purpose of calculating the SV mass. The \ensuremath{M_\text{SV}}\xspace distributions possess specific features depending on the jet flavor, and can be used as templates in a fit to the \ensuremath{M_\text{SV}}\xspace distribution in data to extract the fractions of \cPqc and \cPqb jets, as discussed in Section~\ref{sec:sf}.

The template fit is performed in the \zj sample enriched with HF jets, \ie, in the \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace sample, and the observed number of \zcs ($N_{\PQc}$) and \zbs ($N_{\PQb}$) events are derived. They are corrected for the efficiencies of tagging events, $\epsilon^{\PQc}_{\text{tag}}$ and $\epsilon^{\PQb}_{\text{tag}}$ for $N_{\PQc}$ and $N_{\PQb}$, respectively, to obtain the numbers of \zcs and \zbs events in the \zj sample. The cross section ratios are then calculated as
\begin{equation}\label{eq:rcj}
  \text{R}(\cPqc/\text{j}) = \frac{\sigma(\zcs)}{\sigma(\zj)} = \frac{N_{\PQc}}{N_{\text{jet}}\epsilon^{\PQc}_{\text{tag}}},
\end{equation}
\begin{equation}\label{eq:rbj}
  \text{R}(\cPqb/\text{j}) = \frac{\sigma(\zbs)}{\sigma(\zj)} = \frac{N_{\PQb}}{N_{\text{jet}}\epsilon^{\PQb}_{\text{tag}}},
\end{equation}
\begin{equation}\label{eq:rcb}
  \text{R}(\cPqc/\cPqb) = \frac{\sigma(\zcs)}{\sigma(\zbs)} = \frac{N_{\PQc}\epsilon^{\PQb}_{\text{tag}}}{N_{\PQb}\epsilon^{\PQc}_{\text{tag}}},
\end{equation}
where $N_{\text{jet}}$ is the number of selected \zj events remaining after subtracting background contributions (\ttbar, diboson, and single top) from data. These backgrounds are estimated using simulation. In the above formulas, the integrated luminosity as well as the efficiencies that are related to lepton and \ptmiss requirements in the \zj event selection cancel.

For the differential measurements, the same procedure described here is applied in each jet or \PZ boson \pt interval. Dedicated \ensuremath{M_\text{SV}}\xspace templates are derived for each interval to take into account the dependence of the \ensuremath{M_\text{SV}}\xspace shape on jet kinematic variables. Finally, the cross section ratios are unfolded for various experimental effects, most notably the detector resolution and efficiencies.

\subsection{\texorpdfstring{\PZ{}+HF jets}{Z+HF Jets} event tagging efficiency}\label{subsec:eff}

The efficiencies of tagging \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace events, $\epsilon^{\PQc}_{\text{tag}}$ and $\epsilon^{\PQb}_{\text{tag}}$, are calculated as the ratio between numbers of selected \zcs and \zbs events, respectively, in the \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace and the \zj samples. They are estimated using simulations, which are corrected with data. In the jet \pt range between 30 and 200\GeV the efficiencies vary only slightly and range from 8.3 to 11.3\% for \zcs and from 45.9 to 60.7\% for \zbs events. The \zls mistagging rate increases from 0.3 to 1.0\% in the same \pt range.

\subsection{Estimation of the event yields}\label{sec:sf}
A binned maximum likelihood template fit, based on \ensuremath{M_\text{SV}}\xspace distributions of the leading \pt HF-tagged jets, is used to obtain the numbers of \zcs and \zbs events in the \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace sample. The parameters of interest are the scale factors, \ensuremath{\mathrm{SF}_{\PQc}}\xspace and \ensuremath{\mathrm{SF}_{\PQb}}\xspace, that adjust the MC rates to fit the data, while their uncertainties are treated as nuisance parameters. The \ensuremath{M_\text{SV}}\xspace distributions of the simulated \zcs, \zbs, and \zls categories are normalized to the integrated luminosity of the data sample using an NNLO cross section for the total \zj rate. The top quark and diboson backgrounds, which contribute about 5\% of the events in the \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace sample, are estimated from simulation. The predicted yields of all these processes are shown in Table~\ref{tab:event_counts}.

For each \ensuremath{M_\text{SV}}\xspace bin a Poisson distribution is constructed from the number of observed events, with its mean taken from MC predictions of signal (\zcs and \zbs) and background (\zls, top quark, and diboson) yields. The likelihood is the product of the Poisson distributions and Gaussian (or log-normal) distributions, where the latter are used to constrain the nuisance parameters. The choice of Gaussian or log-normal constraints depends on whether the corresponding systematic uncertainty affects the shape or normalization of the templates, respectively. To obtain a combined result, the electron and muon channel data are fitted simultaneously using a common set of scale factors. After the fit, the numbers of \zcs and \zbs events, $N_{\PQc}$ and $N_{\PQb}$, are obtained from the MC predictions scaled by the \ensuremath{\mathrm{SF}_{\PQc}}\xspace and \ensuremath{\mathrm{SF}_{\PQb}}\xspace factors.

The \ensuremath{M_\text{SV}}\xspace template of \cPqc~jets\xspace in the \zcs events is obtained from simulation. The \cPqc~jet\xspace \ensuremath{M_\text{SV}}\xspace shape is validated with a \ttbar-enriched data sample where only one of the \PW bosons decays to leptons. The other \PW boson decays hadronically with a branching fraction of 33\% for a charm quark in the final state. The event selection requires a well-identified and isolated muon having $\pt > 25\GeV$ and $\abs{\eta} < 2.4$ together with at least four jets, each with $\pt >30\GeV$ and $\abs{\eta} < 2.4$. The \cPqc and \cPqb jet identification is performed with the following procedure. To reduce the combinatorics the best pair (triplet) of jets is chosen by minimizing the reconstructed and nominal mass of the \PW boson (top quark). From this optimization, the \cPqc and \cPqb~jet\xspace candidates from top quark and \PW boson decays are identified. The event is kept if these candidates pass the jet HF tagging requirement described in Section~\ref{sec:sel}. In the resulting sample of the \cPqc~jet\xspace candidates about half have correct flavor assignment whereas the other half constitute mostly \cPqb~jets\xspace that are misidentified as \cPqc~jets\xspace. The \cPqc~jet\xspace \ensuremath{M_\text{SV}}\xspace distribution in data is found by subtracting the backgrounds containing \cPqb~jets\xspace and light jets in the sample.

The \cPqc~jet\xspace \ensuremath{M_\text{SV}}\xspace template from simulation is compared with that observed in the validation sample and agreement is found within the statistical uncertainties as shown in Fig.~\ref{fig:temp_val} (left). The pronounced enhancement seen in the \cPqc~jets\xspace \ensuremath{M_\text{SV}}\xspace distribution near 1.8\GeV is due to charm meson decays.
\begin{figure*}[tb]
  \centering
  \includegraphics[width=0.4\textwidth]{Figure_001-a.pdf}
  \includegraphics[width=0.4\textwidth]{Figure_001-b.pdf}
  \caption{Comparisons of \cPqc~jet\xspace (left) and \cPqb~jet\xspace (right) \ensuremath{M_\text{SV}}\xspace distributions for data and simulation. A shape correction is applied to the data-driven distribution in the right panel to account for the difference between the jets in \ttbar and \zbs processes.}
  \label{fig:temp_val}
\end{figure*}

The \ensuremath{M_\text{SV}}\xspace template for \cPqb~jets\xspace is derived from a high-purity data sample of \ttbar events decaying to final states of \ensuremath{\Pe\PGm}\xspace $+\ge$ 2 jets with at least one b-tagged jet. Leptons must pass similar requirements as those used in the selection of \zj events except for a tighter isolation criterion (other activity with less than 15\% of the lepton transverse momentum, instead of 25\%) to strongly suppress multijet and \wj backgrounds. The \ensuremath{M_\text{SV}}\xspace shape depends on the kinematic distributions of the corresponding jets, therefore the \cPqb~jet\xspace \ensuremath{M_\text{SV}}\xspace templates obtained with the \ttbar data are corrected to account for the difference between the \cPqb~jet\xspace \pt spectra in \ttbar and \zbs events. This correction is derived from simulation by comparing the \cPqb~jet\xspace \ensuremath{M_\text{SV}}\xspace shapes in those two samples of events. It is parameterized as a second-order polynomial function of \ensuremath{M_\text{SV}}\xspace and varies between 3 and 20\% across jet \pt ranges. A comparison between the simulated and data-driven \cPqb~jet\xspace \ensuremath{M_\text{SV}}\xspace distributions are presented in Fig.~\ref{fig:temp_val} (right). This correction procedure is applied in both the inclusive and differential measurements.

The \ensuremath{M_\text{SV}}\xspace modeling of light jets in simulation is checked in the validation sample containing \wj events selected by requiring a well-identified and isolated muon together with at least one jet. Discrimination criteria of \cPqc~jet\xspace versus light jets are applied, resulting in a sample with light jet purity of ${\approx}40\%$. The light jet \ensuremath{M_\text{SV}}\xspace templates in data are derived from the validation sample after subtracting nonlight jet components, which mainly consist of the \wcs events. Good agreement between the data-driven template shape and the simulation is observed.

The scale factors obtained from the combined fit in the inclusive \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace data sample are $\text{SF}_{\text{c}}=0.849 \pm 0.013 \text{ (stat)} \pm 0.064 \text{ (syst)}$ and $\text{SF}_{\text{b}}=0.873 \pm 0.005 \text{ (stat)} \pm 0.013 \text{ (syst)}$. Tables~\ref{tab:sf_fit_1} and~\ref{tab:sf_fit_2} list the scale factors estimated in the jet and \PZ \pt bins. Details on the evaluations of systematic uncertainties in the scale factors are discussed in Section~\ref{sec:syst}. The two channels pass a $\chi^2$ based compatibility check except for the \ensuremath{\mathrm{SF}_{\PQc}}\xspace fluctuation in one jet \pt bin of 50--110\GeV with a $p$-value of ${\approx}0.3\%$. The post-fit \ensuremath{M_\text{SV}}\xspace distributions are shown in Fig.~\ref{fig:fig_postfit_1} for the measurements using the inclusive \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace samples. Examples of the post-fit \ensuremath{M_\text{SV}}\xspace distributions in the muon channel for exclusive jet \pt bins are given in Appendix~\ref{sec:msv_dist}, Fig.~\ref{fig:fig_postfit_2}.

\begin{table*}[ht]
\topcaption{The \ensuremath{\mathrm{SF}_{\PQc}}\xspace and \ensuremath{\mathrm{SF}_{\PQb}}\xspace scale factor fit results for electron, muon, and combined channels in jet \pt bins. The first and second uncertainty values correspond to the statistical and systematic contributions, respectively. The fractions of the observed number of \zcs and \zbs in the total number of \zj events selected in the \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace sample are shown in the parentheses and are determined by applying the scale factors to the corresponding MC events.}
\label{tab:sf_fit_1}
\centering
\cmsTable{
\begin{scotch}{ccccccc}
\multirow{3}{*}{\begin{tabular}{@{}c@{}} Jet \pt bins \\ (\GeVns) \end{tabular} } &\multicolumn{3}{c}{\ensuremath{\mathrm{SF}_{\PQc}}\xspace} & \multicolumn{3}{c}{\ensuremath{\mathrm{SF}_{\PQb}}\xspace}\\
&\multicolumn{3}{c}{(\zc fraction)} & \multicolumn{3}{c}{(\zb fraction)}\\
& Electron & Muon & Combined & Electron & Muon & Combined\\
\hline
30--35&0.91$\pm$0.05$\pm$0.07 & 0.88$\pm$0.03$\pm$0.07 & 0.89$\pm$0.03$\pm$0.06 & 0.83$\pm$0.02$\pm$0.03 & 0.83$\pm$0.01$\pm$0.03 & 0.83$\pm$0.01$\pm$0.03\\
 & (25.4$\pm$1.3$\pm$2.1)\% & (25.8$\pm$1.0$\pm$2.1)\% & (25.6$\pm$0.8$\pm$1.7)\% & (64.8$\pm$1.4$\pm$2.4)\% & (64.2$\pm$1.1$\pm$2.4)\% & (64.5$\pm$0.9$\pm$1.9)\%\\
35--40&0.78$\pm$0.05$\pm$0.08 & 0.79$\pm$0.04$\pm$0.07 & 0.79$\pm$0.03$\pm$0.06 & 0.91$\pm$0.02$\pm$0.03 & 0.87$\pm$0.01$\pm$0.03 & 0.89$\pm$0.01$\pm$0.03\\
 & (21.1$\pm$1.4$\pm$2.0)\% & (22.3$\pm$1.1$\pm$2.0)\% & (21.7$\pm$0.9$\pm$1.7)\% & (69.7$\pm$1.5$\pm$2.6)\% & (68.7$\pm$1.2$\pm$2.4)\% & (69.2$\pm$0.9$\pm$2.1)\%\\
40--50&0.66$\pm$0.04$\pm$0.06 & 0.67$\pm$0.03$\pm$0.07 & 0.67$\pm$0.03$\pm$0.06 & 0.83$\pm$0.01$\pm$0.02 & 0.83$\pm$0.01$\pm$0.02 & 0.83$\pm$0.01$\pm$0.02\\
 & (18.2$\pm$1.2$\pm$1.8)\% & (18.4$\pm$0.9$\pm$1.8)\% & (18.3$\pm$0.7$\pm$1.7)\% & (73.9$\pm$1.3$\pm$1.9)\% & (73.1$\pm$1.1$\pm$1.8)\% & (73.4$\pm$0.8$\pm$1.6)\%\\
50--110&0.89$\pm$0.04$\pm$0.06 & 0.73$\pm$0.03$\pm$0.05 & 0.79$\pm$0.02$\pm$0.05 & 0.89$\pm$0.01$\pm$0.02 & 0.92$\pm$0.01$\pm$0.03 & 0.91$\pm$0.01$\pm$0.03\\
 & (20.3$\pm$0.8$\pm$1.3)\% & (17.5$\pm$0.6$\pm$1.2)\% & (18.6$\pm$0.5$\pm$1.1)\% & (72.9$\pm$1.0$\pm$1.8)\% & (75.1$\pm$0.7$\pm$2.5)\% & (74.1$\pm$0.6$\pm$2.3)\%\\
110--200&0.70$\pm$0.09$\pm$0.06 & 0.85$\pm$0.07$\pm$0.07 & 0.79$\pm$0.06$\pm$0.05 & 0.92$\pm$0.04$\pm$0.04 & 0.81$\pm$0.03$\pm$0.04 & 0.84$\pm$0.02$\pm$0.04\\
 & (18.0$\pm$2.3$\pm$1.6)\% & (21.4$\pm$1.8$\pm$1.7)\% & (20.2$\pm$1.4$\pm$1.4)\% & (71.5$\pm$2.7$\pm$3.1)\% & (67.1$\pm$2.2$\pm$3.2)\% & (68.7$\pm$1.7$\pm$3.0)\%\\
\end{scotch}
}
\end{table*}
\begin{table*}[ht]
\topcaption{The \ensuremath{\mathrm{SF}_{\PQc}}\xspace and \ensuremath{\mathrm{SF}_{\PQb}}\xspace scale factor fit results for electron, muon, and combined channels in \PZ \pt bins. The first and second uncertainty values correspond to the statistical and systematic contributions, respectively. The fraction of the observed number of \zcs and \zbs in the total number of \zj events selected in the \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace sample are shown in the parentheses and are derived by applying the scale factors to the corresponding MC events.}
\label{tab:sf_fit_2}
\centering
\cmsTable{
\begin{scotch}{ccccccc}
\multirow{3}{*}{\begin{tabular}{@{}c@{}} \PZ \pt bins \\ (\GeVns) \end{tabular}} &\multicolumn{3}{c}{\ensuremath{\mathrm{SF}_{\PQc}}\xspace} & \multicolumn{3}{c}{\ensuremath{\mathrm{SF}_{\PQb}}\xspace}\\
&\multicolumn{3}{c}{(\zc fraction)} & \multicolumn{3}{c}{(\zb fraction)}\\
& Electron & Muon & Combined & Electron & Muon & Combined\\
\hline
0--30&0.83$\pm$0.04$\pm$0.12 & 0.78$\pm$0.03$\pm$0.10 & 0.80$\pm$0.03$\pm$0.11 & 0.93$\pm$0.02$\pm$0.02 & 0.91$\pm$0.01$\pm$0.02 & 0.92$\pm$0.01$\pm$0.02\\
 & (22.9$\pm$1.1$\pm$3.3)\% & (21.9$\pm$0.9$\pm$2.9)\% & (22.4$\pm$0.7$\pm$3.1)\% & (67.9$\pm$1.2$\pm$1.7)\% & (68.1$\pm$1.0$\pm$1.7)\% & (67.9$\pm$0.7$\pm$1.6)\%\\
30--50&0.79$\pm$0.04$\pm$0.07 & 0.72$\pm$0.03$\pm$0.06 & 0.75$\pm$0.02$\pm$0.06 & 0.84$\pm$0.01$\pm$0.02 & 0.84$\pm$0.01$\pm$0.02 & 0.84$\pm$0.01$\pm$0.02\\
 & (21.6$\pm$1.0$\pm$1.9)\% & (20.5$\pm$0.8$\pm$1.8)\% & (20.9$\pm$0.6$\pm$1.8)\% & (71.0$\pm$1.1$\pm$1.4)\% & (71.6$\pm$0.9$\pm$1.4)\% & (71.4$\pm$0.7$\pm$1.4)\%\\
50--90&0.92$\pm$0.04$\pm$0.06 & 0.77$\pm$0.03$\pm$0.05 & 0.82$\pm$0.03$\pm$0.05 & 0.85$\pm$0.01$\pm$0.01 & 0.88$\pm$0.01$\pm$0.01 & 0.87$\pm$0.01$\pm$0.01\\
 & (21.0$\pm$1.0$\pm$1.3)\% & (18.5$\pm$0.7$\pm$1.2)\% & (19.5$\pm$0.6$\pm$1.2)\% & (72.0$\pm$1.1$\pm$1.1)\% & (74.0$\pm$0.8$\pm$1.1)\% & (73.2$\pm$0.7$\pm$1.0)\%\\
90--200&0.76$\pm$0.06$\pm$0.05 & 0.90$\pm$0.05$\pm$0.05 & 0.84$\pm$0.04$\pm$0.04 & 0.97$\pm$0.02$\pm$0.02 & 0.90$\pm$0.02$\pm$0.02 & 0.92$\pm$0.01$\pm$0.02\\
 & (17.2$\pm$1.4$\pm$1.0)\% & (20.6$\pm$1.1$\pm$1.2)\% & (19.2$\pm$0.9$\pm$1.0)\% & (73.4$\pm$1.6$\pm$1.3)\% & (69.9$\pm$1.2$\pm$1.3)\% & (71.3$\pm$1.0$\pm$1.2)\%\\
\end{scotch}
}
\end{table*}

\begin{figure*}[htb]
\centering
\includegraphics[width=0.45\textwidth]{Figure_002-a.pdf}
\includegraphics[width=0.45\textwidth]{Figure_002-b.pdf}
\caption{Secondary vertex invariant mass distributions for the electron (left) and muon (right) channels derived from fits using the inclusive \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace data sample. The post-fit uncertainty bands indicate the total uncertainties, added in quadrature, of the best-fit values of signal and background process rates.}
\label{fig:fig_postfit_1}
\end{figure*}

\section{Unfolding}\label{sec:unfolding}

The unfolding procedure corrects the measured cross section ratios for effects related to the detector response and the event reconstruction procedures, which can lead to migrations between bins and therefore alter the true distributions. The bin-by-bin migrations are corrected by the response matrices, which quantify the migration probability between the measured and true values of a given observable (jet or \PZ \pt). These matrices are derived in simulation by comparing the final-state objects (jets and leptons) at the pre-reconstruction (``MC-particle") and reconstruction levels.

At the MC-particle level (denoted as ``particle level"), leptons are stable particles from \PZ boson decays, dressed by adding the momenta of all photons within $\Delta R < 0.1$ around the lepton directions. The particle-level jets are formed from stable particles (c$\tau>1\unit{cm}$), except neutrinos, and overlapping leptons from \PZ boson decays, using the same anti-\kt jet algorithm used for reconstructed jets.

The \PZ boson mass and \pt at the particle level are calculated using the two leptons originating from this boson. The fiducial volume is defined by the particle-level leptons and jets with the same kinematic requirements (\pt, $\eta$, and dilepton invariant mass) used in the measurement.

The response matrix is constructed using MC \zj samples. The reconstructed jets and a pair of electrons or muons are spatially matched to the corresponding particle-level objects by requiring that they are within $\Delta R < 0.2$. In addition, the flavor of the reconstructed jets and the matched particle-level jets must be the same. Events that have reconstructed objects without matched particle-level objects are included in the background category and are subtracted from the sample. The acceptance and efficiency corrections account for other events that have particle-level objects in the fiducial volume but no matching reconstructed objects.

For the inclusive measurement, the acceptance corrections are derived from simulation and defined as the ratios between the number of selected events at the reconstruction level and the number of generated events within the fiducial volume. These acceptance correction factors, which depend on the jet flavor, are applied to the measured cross section ratios.

To unfold the differential distributions, the \textsc{TUnfold}\xspace package~\cite{Schmitt}, which is based on a least-square fit, is used. The unfolding procedure, which solves for a well-conditioned unfolding problem in this case, is performed without regularization to avoid potential biases toward MC spectra. The data distributions of \zcs, \zbs, and \zj are unfolded simultaneously to include the correlations between the denominator and numerator when deriving the unfolded ratios. The numbers of bins in the unfolded distributions are about half of those used in data to maintain the stability of the unfolding procedure. The combined response matrix used in the simultaneous unfolding is constructed from individual jet category matrices. The \textsc{TUnfold}\xspace package provides unfolded distributions together with a covariance matrix, which is used to estimate the uncertainties in the unfolded cross section ratios. The unfolding procedure is checked with closure tests and bias studies using MC samples. In the closure test, response matrices are derived using one-half of the sample and the unfolding is performed on the other half. Within statistical uncertainties, the unfolded and MC truth distributions agree with each other. In the bias studies, a pull distribution is constructed by performing the unfolding on a set of ${\approx}100$ MC sub-samples. The unfolding procedure converges and shows no bias.

\section{Systematic uncertainties}\label{sec:syst}

The systematic uncertainties include experimental sources that affect the shape or normalization of templates in the scale factor fits, and the heavy-flavor tagging efficiencies. The unfolded results contain additional uncertainties related to the unfolding procedure. The following systematic uncertainties are considered in the analysis:

{\textit{Jet energy scale and resolution correction:}} The reconstructed jet energy is corrected using a factorized model to compensate for the nonlinear and nonuniform response in the calorimeters as detailed in Ref.~\cite{Khachatryan:2016kdb}. Since the JER is different in data and simulation, the jet energy in simulation is spread to match the resolution observed in data. Both the JES and JER corrections affect the shape of \ensuremath{M_\text{SV}}\xspace distributions used in the scale factor fits. Therefore, they contribute to the uncertainties in the \zqc and \zbs event yields.

{\textit{Pileup weighting:}} The distribution of the number of pileup events in simulation is weighted to match that in data. The corresponding uncertainty is estimated by varying the total $\Pp\Pp$ inelastic cross section by 4.6\% based on the measurement described in Ref.~\cite{ppinelastic}. Since the shapes of \ensuremath{M_\text{SV}}\xspace templates are affected by the pileup weighting, this uncertainty source contributes to the \zcs and \zbs event yields as well.

{\textit{Gluon splitting:}} Particles from a pair of collimated \cPqc or \cPqb quarks may end up in the same reconstructed jet, which can affect the shape of \ensuremath{M_\text{SV}}\xspace template. To quantify the corresponding uncertainties in the scale factor fit, the fraction of MC events with gluon splitting is varied by 50\%, which is about three times the experimental uncertainty in the gluon splitting rate measured at LEP~\cite{gcc,gbb}. The resulting variations in MC \ensuremath{M_\text{SV}}\xspace shape is propagated to the scale factor fit.

{\textit{Background rates:}} The \ttbar, single top quark, and diboson backgrounds are estimated in simulation using NNLO and NLO cross sections to normalize the event rates. The uncertainties in the \ttbar and diboson background contributions are obtained by varying their production cross sections by 5.5 and 3.2\%, respectively. The uncertainty in the single top backgrounds is ignored because these backgrounds represent a very small fraction (${<}1\%$) of the total event sample.

{\textit{Statistical uncertainties of \ensuremath{M_\text{SV}}\xspace templates:}} A systematic uncertainty is associated to the limited number of events in the MC samples used to define the template shapes. To estimate the corresponding uncertainty, an ensemble of the \ensuremath{M_\text{SV}}\xspace templates has been created where the bin contents have been modified by additional statistical fluctuations.

{\textit{Correction of the \cPqb~jet\xspace \ensuremath{M_\text{SV}}\xspace template:}} This systematic uncertainty is related to the ad hoc shape correction function used to derive the \cPqb~jet\xspace \ensuremath{M_\text{SV}}\xspace template from control samples in data. This correction, parameterized as a second order polynomial, accounts for the difference in shape of \ensuremath{M_\text{SV}}\xspace distributions in \ttbar and \zj events. The uncertainty of the shape correction is estimated by changing the polynomial functional forms.

{\textit{Heavy-flavor tagging efficiency:}} The HF tagging efficiencies for \cPqc and \cPqb~jets\xspace are estimated in simulation and corrected by the efficiency scale factors as described in Section~\ref{subsec:eff}. The systematic uncertainties of the efficiency scale factors of \cPqc~jets\xspace and \cPqb~jets\xspace with $30 < \pt < 100\GeV$ and $\abs{\eta} < 2.4$ are ${\approx}3.5\%$ and ${\approx}1.4\%$, respectively~\cite{csv}.

{\textit{Missing transverse momentum selection efficiency:}} This uncertainty source accounts for possible differences in the \ptmiss selection ($\ptmiss < 40\GeV$) efficiencies for \zj and \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace events. The effect comes from contributions of semileptonic decays of HF hadrons in \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace events, which results in large \ptmiss values. Therefore, the efficiencies tend to be lower for \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace events by ${\approx}1\%$ at high jet and \PZ boson \pt regions compared to those of \zj events. An uncertainty of 1.5\% is included in the R(c/j) and R(b/j) differential results for jet (\PZ boson) \pt bins where $\pt>60$ (90)\GeV.

{\textit{PDF and \ensuremath{\mu_\text{R}}\xspace, \ensuremath{\mu_\text{F}}\xspace scale uncertainties:}} These uncertainty sources affect the unfolding correction described in Section~\ref{sec:unfolding}, which is based on the \zj MC samples. The unfolding is performed with different PDF replicas and alternative choices of the renormalization and factorization scales. The uncertainties are obtained from variations of the unfolded results and they are less than 2.5\%, 2.8\%, and 2.9\% in all jet and \PZ \pt bins for R(c/j), R(b/j), and R(c/b), respectively.

{\textit{Parton shower and hadronization model:}} The unfolding procedure is based on response matrices constructed from the \zj simulation sample described in Section~\ref{sec:sample}. This sample uses \PYTHIA to simulate the parton shower and hadronization. An alternative model is provided by the \HERWIGpp generator~\cite{herwig}. The uncertainties in parton shower and hadronization modeling are estimated by comparing the unfolded results using response matrices from those two models. They are less than 3\% for all differential cross section ratios.

Table~\ref{tab:unc_sfs} summarizes the effects of systematic uncertainty sources on the \ensuremath{\mathrm{SF}_{\PQc}}\xspace and \ensuremath{\mathrm{SF}_{\PQb}}\xspace shown in Tables~\ref{tab:sf_fit_1} and~\ref{tab:sf_fit_2}. They are quantified as the differences in quadrature between scale factor uncertainties obtained in two fits: the nominal one where all parameters are allowed to float, and an alternative fit where the nuisance parameter corresponding to the uncertainty source of interest is fixed. The uncertainties from the scale factors and HF tagging efficiency together with the statistical uncertainties of the cross section ratios are listed in Table~\ref{tab:unc_ratios}.

In the unfolded differential results, the uncertainties of the measurements described here are included in the data covariance matrix, which is used to build a least squares fit of the unfolding. An error covariance matrix for the unfolded distributions is estimated. This includes the uncertainties from the data, response matrix, and the unfolding procedure.

\begin{table}[htb]
\topcaption{Systematic uncertainties in the scale factor measurements. The uncertainty ranges correspond to variations across jet and \PZ \pt bins.}
\label{tab:unc_sfs}
\centering
\begin{scotch}{ccc}
 & \ensuremath{\mathrm{SF}_{\PQc}}\xspace & \ensuremath{\mathrm{SF}_{\PQb}}\xspace \\
 \hline
JES, JER               & 1.7--7.4\%         & 0.3--2.1\%\\
Template statistics    & 2.4--6.1\%         & 0.6--2.7\%\\
Gluon splitting        & 2.2--3.9\%         & 0.5--2.0\%\\
Pileup weighting     & 1.6--2.8\%         & 0.3--1.0\%\\
Background uncertainty & 0.3--1.0\%         & 0.4--1.2\%\\
\cPqb~jet\xspace \ensuremath{M_\text{SV}}\xspace correction   & 0.2--1.6\%         & 0.2--0.8\%\\
Total systematic uncertainty & 4.8--12.5\% & 1.1--4.9\%\\
\end{scotch}
\end{table}

\begin{table}[htb]
\topcaption{The systematic uncertainties in the cross section ratio measurements. The uncertainty ranges correspond to variations across jet and \PZ \pt bins.}
\label{tab:unc_ratios}
\centering
\begin{scotch}{cccc}
 & R(c/j) & R(b/j) & R(c/b)\\
\hline
Scale factor measurement & 5.4--13.8\% & 1.4--4.4\% & 5.6--12.6\%\\
HF tagging               & 3.8--4.6\%  & 1.1--1.5\% & 4.9--6.1\%\\
Statistical uncertainty  & 1.6--7.5\%  & 0.6--3.0\% & 1.8--8.6\%\\
\end{scotch}
\end{table}

\section{Results}\label{sec:result}

The observed and corrected (for the acceptance and efficiency) cross section ratios for the inclusive measurements are summarized in Tables~\ref{tab:rat_results_1} and~\ref{tab:rat_unfolded}, respectively. The measured differential cross section ratios are presented in Appendix~\ref{sec:diff_xsec}, Tables~\ref{tab:rat_results_2} and~\ref{tab:rat_results_3}.

\begin{table*}[ht]
\topcaption{Cross section ratios measured in the electron and muon channels, along with the combined results. The first and second uncertainty values correspond to the statistical and systematic contributions, respectively.}
\label{tab:rat_results_1}
\centering
\cmsTable{
\begin{scotch}{cccc}
  &                                                Electron &          Muon &              Combined\\
\hline
R(c/j) & 0.098 $\pm$ 0.002 $\pm$ 0.009 & 0.094 $\pm$ 0.002 $\pm$ 0.008  & 0.095 $\pm$ 0.002 $\pm$ 0.008\\
R(b/j) & 0.0546 $\pm$ 0.0005 $\pm$ 0.0010 & 0.0538 $\pm$ 0.0004 $\pm$ 0.0010 & 0.0541 $\pm$ 0.0003 $\pm$ 0.0011\\
R(c/b) & 1.80 $\pm$ 0.05 $\pm$ 0.17 & 1.75 $\pm$ 0.04 $\pm$ 0.16 & 1.76 $\pm$ 0.03 $\pm$ 0.16 \\
\end{scotch}
}
\end{table*}

\begin{table*}[ht]
\topcaption{Unfolded cross section ratios in the electron and muon channels, along with the combined results. The first and second uncertainty values correspond to the statistical and systematic contributions, respectively.}
\label{tab:rat_unfolded}
\centering
\begin{scotch}{cccc}
   &                                                Electron &          Muon &              Combined\\
\hline
R(c/j) & 0.105 $\pm$ 0.003 $\pm$ 0.009 & 0.101 $\pm$ 0.002 $\pm$ 0.009 & 0.102 $\pm$ 0.002 $\pm$ 0.009 \\
R(b/j) & 0.0639 $\pm$ 0.0006 $\pm$ 0.0015  & 0.0629 $\pm$ 0.0005 $\pm$ 0.0014 & 0.0633 $\pm$ 0.0004 $\pm$ 0.0015 \\
R(c/b) & 1.65 $\pm$ 0.04 $\pm$ 0.15 & 1.61 $\pm$ 0.04 $\pm$ 0.15 & 1.62 $\pm$ 0.03 $\pm$ 0.15 \\
\end{scotch}
\end{table*}

The unfolded differential cross section ratios, R(c/j), R(b/j), and R(c/b), versus the jet and \PZ boson \pt are shown in Figs.~\ref{fig:diff_cj_comp},~\ref{fig:diff_bj_comp}, and ~\ref{fig:diff_cb_comp}, respectively. The results are compared with predictions from the \textsc{mg}5\_a\textsc{MC}\xspace and \MCFM programs~\cite{MCFM1,MCFM2,MCFM3}, both at LO and NLO. The renormalization and factorization scales in the matrix element and the PDF uncertainties are included in these predictions. For the former, the scales are varied between 0.5 and 2 times their nominal value such that the \ensuremath{\mu_\text{R}}\xspace/\ensuremath{\mu_\text{F}}\xspace ratio is kept between 0.5 and 2. This conventional choice is implemented in the CMS-default settings for generating samples to estimate the theoretical \textsc{mg}5\_a\textsc{MC}\xspace LO and NLO cross sections. The uncertainty due to the scales is taken to be the envelope of these predictions. In addition, for the \MCFM calculation, the constraint on the \ensuremath{\mu_\text{R}}\xspace/\ensuremath{\mu_\text{F}}\xspace ratio is dropped, \ie, the scales are varied independently. This more conservative choice is motivated by the fact that the \ensuremath{\PZ\hspace{-.25em}+\hspace{-.15em}\text{HF~jets}}\xspace cross sections as functions of the renormalization and factorization scales have opposite trends~\cite{Campbell:2003dd}. The \MCFM error bands in Figs.~\ref{fig:diff_cj_comp}--\ref{fig:diff_cb_comp} correspond to this choice of scale variation. The uncertainties due to the scales in the cross section ratios are obtained by adding uncertainties in the numerator and denominator in quadrature, \ie, they are assumed to be uncorrelated. The PDF uncertainty is evaluated by changing the replicas of the PDF set.

The LO cross sections are computed using \textsc{mg}5\_a\textsc{MC}\xspace interfaced with \PYTHIA through the \kt-MLM matching scheme~\cite{Alwall:2007fs,Alwall:2008qv}. The LO matrix element calculations include processes with up to 4 outgoing partons. The NNPDF 3.0 LO PDF set is used and the matching scale together with the strong coupling constant \alpS at the \PZ boson mass are set at 19\GeV and 0.130, respectively. The multileg \textsc{mg}5\_a\textsc{MC}\xspace generator interfaced with \PYTHIA using the FxFx matching scheme evaluates the cross section ratios at NLO precision. The choice of parameters is described in Section~\ref{sec:sample}.

The \MCFM generator is used to perform calculations of the cross sections and cross section ratios at the parton level in the 5FS. The \zj cross sections are evaluated by a simple cone algorithm with a radius of 0.4 (\ie, partons are merged if the distances, $\Delta R$, between them are less than 0.4). The central values for the cross sections are evaluated at \ensuremath{\mu_\text{R}}\xspace and \ensuremath{\mu_\text{F}}\xspace set to the mass of the \PZ boson. In addition, the NLO \MCFM results are shown for two PDFs, NNPDF 3.0 and MMHT14~\cite{MMHT}, along with the \MCFM LO cross section ratios. The values of \alpS are taken from those PDFs. Table~\ref{tab:rat_prediction} shows the predicted inclusive cross section ratios from \textsc{mg}5\_a\textsc{MC}\xspace and \MCFM.

\begin{table*}[htb]
\topcaption{Predicted cross section ratios from \textsc{mg}5\_a\textsc{MC}\xspace and \MCFM at LO and NLO accuracy. The first and second sets of uncertainties correspond to PDF and scale variations, respectively. The scale uncertainties for \MCFM with \ensuremath{\mu_\text{R}}\xspace/\ensuremath{\mu_\text{F}}\xspace ratio kept between 0.5 and 2 are in the parentheses.}
\label{tab:rat_prediction}
\centering
\cmsTable{
\begin{scotch}{ccccc}
& \textsc{mg}5\_a\textsc{MC}\xspace MG5\_aMC (NLO, FxFx) & \MCFM (NLO) & \textsc{mg}5\_a\textsc{MC}\xspace (LO, MLM) & \MCFM (LO) \\
\hline
\rule{0pt}{3ex}
R(c/j) & 0.111 $\pm$ 0.003 $^{+0.010}_{-0.011}$ & 0.090 $\pm$ 0.003 $^{+0.010}_{-0.012}$ ($^{+0.008}_{-0.007}$) & 0.103 $\pm$ 0.003 $^{+0.028}_{-0.026}$ & 0.087 $\pm$ 0.003 $^{+0.025}_{-0.022}$\\
\rule{0pt}{3ex}
R(b/j) & 0.067 $\pm$ 0.002 $\pm$ 0.006 & 0.068 $\pm$ 0.002 $^{+0.008}_{-0.011}$ ($\pm$0.006) & 0.062 $\pm$ 0.002 $^{+0.018}_{-0.015}$ & 0.071 $\pm$ 0.002 $^{+0.023}_{-0.021}$ \\
\rule{0pt}{3ex}
R(c/b) & 1.64 $\pm$ 0.05 $^{+0.15}_{-0.16}$ & 1.33 $\pm$ 0.04 $^{+0.16}_{-0.21}$ ($^{+0.10}_{-0.12}$) & 1.67 $\pm$ 0.06 $^{+0.54}_{-0.40}$ & 1.20 $\pm$ 0.04 $^{+0.42}_{-0.38}$ \\
\end{scotch}
}
\end{table*}

\begin{figure*}[htb]
\includegraphics[width=0.45\textwidth]{Figure_003-a.pdf}
\includegraphics[width=0.45\textwidth]{Figure_003-b.pdf}
\caption{Unfolded, particle-level \textsc{mg}5\_a\textsc{MC}\xspace, and parton-level \MCFM R(c/j) cross section ratios versus jet (left) and \PZ boson (right) transverse momentum. The vertical error bars for the data points are statistical while the hatched band represents the total uncertainties. The predictions are slightly shifted along the $x$-axis for readability in the upper plots, and their total PDF and scale uncertainties are shown as error bands in the ratio plots.}
\label{fig:diff_cj_comp}
\end{figure*}

A few comments are in order when comparing data with various predictions. The \textsc{mg}5\_a\textsc{MC}\xspace predictions for the cross section ratios are higher in most of the bins, although still compatible with the data given the large uncertainties, except for the R(c/j) versus jet \pt, where the deviations are more pronounced. The data are better described with \textsc{mg}5\_a\textsc{MC}\xspace at LO compared to \textsc{mg}5\_a\textsc{MC}\xspace at NLO. These observations are similar to those reported in previous measurements at 8\TeV~\cite{ZbCMS,ZCciemat}. The \MCFM predictions for R(c/j) and R(b/j) disagree with data at high jet and \PZ \pt, except for R(c/j) versus jet \pt, where in general there is good agreement with LO or NLO calculations, and for both PDFs considered. For R(c/b), however, all theoretical predictions are consistent with the measured ratios, except for the \MCFM prediction for the highest \PZ boson \pt bin.  The difference between the parton- and particle-level jets may affect the \MCFM predictions, although the corresponding effects are significantly reduced or vanish in the cross section ratios. Alternatively, higher order pQCD calculations might be needed to describe the data.

\begin{figure*}[htb]
\includegraphics[width=0.45\textwidth]{Figure_004-a.pdf}
\includegraphics[width=0.45\textwidth]{Figure_004-b.pdf}
\caption{Unfolded, particle-level \textsc{mg}5\_a\textsc{MC}\xspace, and parton-level \MCFM R(b/j) cross section ratio versus jet (left) and \PZ boson (right) transverse momentum. The vertical error bars for the data points are statistical while the hatched band presents the total uncertainties. The predictions are slightly shifted along the $x$-axis for readability in the upper plots, and their total PDF and scale uncertainties are shown as error bands in the ratio plots.}
\label{fig:diff_bj_comp}
\end{figure*}

\begin{figure*}[htb]
\includegraphics[width=0.45\textwidth]{Figure_005-a.pdf}
\includegraphics[width=0.45\textwidth]{Figure_005-b.pdf}
\caption{Unfolded, particle-level \textsc{mg}5\_a\textsc{MC}\xspace, and parton-level \MCFM R(c/b) cross section ratio versus jet (left) and \PZ boson (right) transverse momentum. The vertical error bars for the data points are statistical while the hatched band represents the total uncertainties. The predictions are slightly shifted along the $x$-axis for readability in the upper plots, and their total PDF and scale uncertainties are shown as error bands in the ratio plots.}
\label{fig:diff_cb_comp}
\end{figure*}

\clearpage
\section{Summary}{\label{sec:sum}}
Ratios of cross sections, $\sigma(\zcs)/\sigma(\zj)$, $\sigma(\zbs)/\sigma(\zj)$, and $\sigma(\zcs)/\sigma(\zbs)$ in the associated production of a \PZ boson with at least one charm or bottom quark jet have been measured in proton-proton collisions at $\sqrt s=13\TeV$ using 35.9\fbinv of data collected by the CMS experiment at the LHC. The fiducial volume of the measurement is defined by $\pt>30\GeV$ and $|\eta|<2.4$ for the jets, where \pt and $\eta$ represent transverse momentum and pseudorapidity, respectively. The \PZ bosons are selected within the mass range of 71 and 111\GeV requiring leptons (electrons or muons) with $\pt > 25\GeV$ and $\abs{\eta} < 2.4$. The measured values are $\sigma(\zcs)/\sigma(\zj) = 0.102 \pm 0.002 \pm 0.009$, $\sigma(\zbs)/\sigma(\zj) = 0.0633 \pm 0.0004 \pm 0.0015$, and $\sigma(\zcs)/\sigma(\zbs) = 1.62 \pm 0.03 \pm 0.15$. Results for the inclusive and differential cross section ratios as functions of jet and \PZ boson transverse momentum are compared with predictions from leading and next-to-leading order perturbative quantum chromodynamics calculations. These are the first results of this kind at 13\TeV.

\begin{acknowledgments}
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and NSFC (China); COLCIENCIAS (Colombia); MSES and CSF (Croatia); RPF (Cyprus); SENESCYT (Ecuador); MoER, ERC IUT, PUT and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); NKFIA (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); MES (Latvia); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pakistan); MSHE and NSC (Poland); FCT (Portugal); JINR (Dubna); MON, RosAtom, RAS, RFBR, and NRC KI (Russia); MESTD (Serbia); SEIDI, CPAN, PCTI, and FEDER (Spain); MOSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); ThEPCenter, IPST, STAR, and NSTDA (Thailand); TUBITAK and TAEK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA).

\hyphenation{Rachada-pisek} Individuals have received support from the Marie-Curie program and the European Research Council and Horizon 2020 Grant, contract Nos.\ 675440, 752730, and 765710 (European Union); the Leventis Foundation; the A.P.\ Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation \`a la Recherche dans l'Industrie et dans l'Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium) under the ``Excellence of Science -- EOS" -- be.h project n.\ 30820817; the Beijing Municipal Science \& Technology Commission, No. Z191100007219010; the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Deutsche Forschungsgemeinschaft (DFG) under Germany's Excellence Strategy -- EXC 2121 ``Quantum Universe" -- 390833306; the Lend\"ulet (``Momentum") Program and the J\'anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, the New National Excellence Program \'UNKP, the NKFIA research grants 123842, 123959, 124845, 124850, 125105, 128713, 128786, and 129058 (Hungary); the Council of Science and Industrial Research, India; the HOMING PLUS program of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, the Mobility Plus program of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/02861, Sonata-bis 2012/07/E/ST2/01406; the National Priorities Research Program by Qatar National Research Fund; the Ministry of Science and Education, grant no. 14.W03.31.0026 (Russia); the Programa Estatal de Fomento de la Investigaci{\'o}n Cient{\'i}fica y T{\'e}cnica de Excelencia Mar\'{\i}a de Maeztu, grant MDM-2015-0509 and the Programa Severo Ochoa del Principado de Asturias; the Thalis and Aristeia programs cofinanced by EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand); the Kavli Foundation; the Nvidia Corporation; the SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA). \end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
International weekly
Results of Zelensky's visits to France and Germany
The President of Ukraine, Volodymyr Zelensky arrived in Paris on an official visit. In the French capital, he held talks with his French counterpart, Emmanuel Macron. During the meeting, the parties discussed the war in Donbass, the situation with the Ukrainian prisoners in the Kremlin and cooperative relations. Zelensky once again stressed that the ceasefire in Donbass is his main priority. He is not going to establish peace by military means, but by diplomatic and sanctions. Macron assumes that Ukraine has already begun negotiations with the militants. However, Zelensky later said that it is not about negotiations with the occupiers, but the contacts will be only within the framework of the Minsk format. Macron, for his part, assured that France will support Ukraine in all its intentions to end the war.
According to Macron, France is ready to hold a meeting in the Normandy format. However, before that, France must see that the parties to the conflict fulfill their obligations. The French President also said that Paris had already previously discussed with German Chancellor, Angela Merkel and with Russian President, Vladimir Putin, which gestures and elements that "continue the Minsk process in order to resume the functioning of the Normandy format" could be.
Zelensky, for his part, stressed that the Minsk agreements and the release of Ukrainian prisoners run parallel to one another, and they needn't to be mixed. Therefore, Ukraine in parallel will continue "Minsk", and then will return to the Normandy format. The Ukrainian President stressed that he wants not only to end the war in Donbass, but to return the Ukrainian prisoners in the Kremlin to their Homeland. Zelensky and Macron discussed the return of 24 sailors captured by Russia on Azov Sea. Macron, for his part, stressed that the issue of the release of Ukrainians for him and his country is important and is in the field of his attention. At the same time, the politician reaffirmed about their support of efforts for their release.[1]
Volodymyr Zelensky believes that the Parliamentary Assembly of the Council of Europe (PACE) has no reason to return the Russian delegation. At the same time, the Ukrainian President stressed that Europe cannot feel safe as long as Russia pretends that international norms do not exist. Macron said that France will continue to put pressure on Russia in the future, but this does not apply to sanctions in the Council of Europe, as it is not the Russian state that suffers from them, but its citizens.
After an official visit to France and a meeting with Emmanuel Macron, President Volodymyr Zelensky went to another European state – Germany. On June 18, the Ukrainian leader met with German Chancellor, Angela Merkel, President Frank-Walter Steinmeier and President of the Bundestag, Wolfgang Schäuble held talks with representatives of German business circles. As with the President of France, the meetings with the German leaders were held in a friendly atmosphere and with mutual support. But the parties discussed the same sensitive issues – the situation in Donbass, anti-Russian sanctions, "Nord Stream - 2", the Normandy format of negotiations.[2]
The minutes of Zelensky's meeting with the Chancellor provided for a number of official events and honors, as it should be at the highest state level. At the final press conference, the parties made a number of important statements. From the rostrum of Chancellor Volodymyr Zelensky appealed to those German entrepreneurs and politicians who advocate the lifting or easing of sanctions against the Kremlin's aggression: «Those who are campaigning for the lifting of sanctions, I urge you to visit the Donbass and see how much grief this war has brought to the Ukrainian people. Look at the Crimea, which has turned from a tourist region and a natural pearl into a real military camp. We did not start this war, but we dream and fight for its completion every day». Zelensky once again stressed in the European capital that anti-Russian sanctions is "the only way to settle this conflict without bloodshed. Merkel assured that sanctions against Russia will not be cancelled until the situation in Donbass will not move from the dead point in the direction of settlement and ceasefire. The same applies to sanctions for the annexation of Crimea.
As for Russia's return to the Council of Europe, Merkel noted this possibility when the aggressor fulfills certain obligations: "As for Russia's return to the Council of Europe, we had different opinions. We had to weigh two things. First of all, it is a violation of international rights against Ukraine. This is a problem that cannot be ignored by the international community. But Russia's return requires certain conditions to be met, it will not be realized at any cost."
The Chancellor also confirmed the agreement to resume the dialogue in the Normandy Four format with the participation of France, Germany, Ukraine and Russia: "We are ready and looking for an opportunity to meet as soon as possible. On July 12, there will be a meeting of advisers in the Minsk format." "The preservation of the transit of Russian gas through Ukraine, its accumulation in Ukrainian storage facilities is a guarantee of energy security of Ukraine and Europe. As you know our contract for the transit of Russian gas ends at the end of this year. But we are negotiating now, and I think that our groups will sit down in the near future, and I am sure that we will agree. And no one in Ukraine will twist their hands." "It is no secret that our positions regarding the "Nord Stream 2" project are diametrically opposed. At the same time, we are grateful for the readiness of Germany for a substantive dialogue on this difficult issue."
At meetings with German President, Frank-Walter Steinmeier and President of the Bundestag, Wolfgang Schäuble, Volodymyr Zelensky raised the issue of infrastructure rehabilitation of Donbass and humanitarian assistance of Europe in this process. The President also touched on the issue of the release of Ukrainian sailors and prisoners of war held by Russia. With the German business community Zelensky discussed further reforms in Ukraine, the fight against corruption and the potential that the country can give to the European market.
The practical result of the meetings in Berlin (as well as in Paris) was the announcement of negotiations within the Normandy Four format. Volodymyr Zelensky counts on the resuscitation of the format and the effectiveness of a new conversation with the Russians. But the main obstacle is that officially Russia is not ready to make advances for Ukraine. The Kremlin openly took a wait-and-see attitude, counting on the manifestation of loyalty from the new government and Zelensky administration. In turn, the President of Ukraine declared that he doesn't intend to trade territories with the aggressor. The Kremlin's reaction to Zelensky's position is eloquently evidenced not even by what sounds on behalf of Putin's speaker Dmitry Peskov, but by what is happening in the occupied territories and the demarcation line in recent months.[3]
Continuous searches and arrests of the Crimean Tatars, sentences to five inhabitants of the peninsula with imprisonment from 12 to 17 years for political beliefs, daily violation of a ceasefire regime and death of soldiers of the Armed Forces of Ukraine is a position of Russia towards Ukraine. In other words, it does not change. Which means that there are no talks about peace. The fact that Kyiv enlists the support of Europe is certainly important and correct. But if Volodymyr Zelensky is interested in moving the process from a dead point, he should look for solutions that will force Russia to peace, or encourage for this purpose.[4]
Thus, Zelensky's foreign trips to the main European states took place. The newly elected President of Ukraine adequately presented the position of our state, which testified to the immutability of our foreign policy. However, although France and Germany welcomed the Minsk process, Normandy format, the release of Ukrainian prisoners of war and sanctions on the Russian Federation, in the end, both states were not heeded the call of Zelensky not to return Russia to the PACE. Therefore, now the new government must decide how it should strengthen its position and enlist the support of European friends in the future.
[1]https://24tv.ua/zustrich_zelenskogo_ta_makrona_17_06_2019_pidsumki_foto_video_zustrichi_n1166536
[3]https://ua.news/ua/volodymyr-zelenskyj-v-berlini-pidsumky-zustrichej-z-nimetskymy-lideramy/
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redpajama_set_name: RedPajamaCommonCrawl


text:
The Canelo History LogoThe Canelo History logo is a block with a bomber airplane, next to the words 'Canelo History'.
The Longest Battle
by Richard Hough
This is the story of the greatest naval conflict in history
'The Second World War demanded more of its sailors than any other war in history, in endurance and unremitting need to face danger - danger from increasingly lethal weapons and an ever-increasing need for vigilance by day and night.'
The war at sea - the longest battle of the Second World War - never ceased. From the Arctic Circle to the Pacific, the enemy threat was ever-present, on the surface, in the skies, and lurking beneath the waves.
In this comprehensive and compelling history, Richard Hough brings the titanic struggle to life. Using personal accounts from veterans of all sides, his book tells the story of the Second World War at sea, including the Battle of the Atlantic and the U-boat menace, the infamy of Pearl Harbor, the American triumph at Midway, naval operations in support of D-Day, and the greatest naval battle of all time, Leyte Gulf.
The definitive book about naval power in the Second World War, Richard Hough's masterpiece is essential reading for followers of Max Hastings and James Holland.
'We are in Richard Hough's debt' New York Times
'Utterly absorbing' Financial Times
Publication Date: 21st October 2021


Sorry, I missed this completely. The PHP announcement mailing list isn't as reliable as I would like to have seen.
Fixed safe_mode validation inside tempnam() when the directory path does not end with a /).
Fixed a possible open_basedir/safe_mode bypass in session extension identified by Grzegorz Stachowiak.
Read everything on this release in the 5.2.13 Release notes. I've tested it on one of my test machines without any issues.
The other release was 5.3.2 on the 4th of march 2010 as a regular maintenance release. It includes the fixes from 5.2.13 as described above. Read the 5.3.2 Release notes for everything that is covered in this release. Again tested this on one of my test machines without any problem.
For instructions on how to upgrade your PHP installation please read: Upgrading PHP.


text:
Q: Import many users into SimpleMembershipProvider I am using MVC4+SimpleMemebershipProvider and have my own profile table. In my project I have functionality to import users into my application. Everything is fine until number of importing users is quite small (up to 100), but for example importing 1000 take ages. To be precised I am trying to synchronize company user database with my own (it is not always an Active Directory) and I am using CSV file to be flexible.
I see following solutions:

*

*Extend membership provider (probably by copy it code, because some functions are private) to add functionality of "bulk insert"

*Write my own membership provider

So my questions are: did somebody did something like this before? Do I have other alternatives?
p.s. I founded Code First Membership Provider, but this solution does not support methods like: reset password, registration with confirmation, etc.

redpajama_set_name: RedPajamaStackExchange


text:
package forms

import models.amendModels.AmendPensionsTakenBetweenModel
import play.api.data.Forms._
import play.api.data._

object AmendPensionsTakenBetweenForm extends CommonBinders {

  def amendPensionsTakenBetweenForm = Form (
    mapping(
      "amendedPensionsTakenBetween" -> nonEmptyText,
      "amendedPensionsTakenBetweenAmt" -> yesNoOptionalBigDecimal,
      "protectionType" -> text,
      "status" -> text
    )(AmendPensionsTakenBetweenModel.apply)(AmendPensionsTakenBetweenModel.unapply)
  )
}

redpajama_set_name: RedPajamaGithub


HF Mechanical Services offers a full domestic and commercial plumbing service across the UK. A core part of our Mechanical Services division, our experienced and professional team guarantee both private customers and contractors a superior service. Covering all aspects of domestic and commercial plumbing including installation and maintenance, we have the experience to exceed your needs.
As part of our Domestic and Commercial Plumbing services, HF Group also offers a full repair service and emergency call out service that covers all plumbing and drainage services.
HF Group offers a fully design and installation service for bathrooms across the UK. Our team of bathroom fitters have fitted hundreds of new bathroom suite across Scotland, England and Ireland. We install all types of bathroom and have built a reputation for exceeding our customers expectations. As a company with over three century in business – reputation and quality of work means everything to us and we constantly strive to ensure that the design and installation of bathrooms by our expert team is done to the highest standard.
Air conditioning systems provides an efficient and effective way of heating and cooling commercial or industrial properties and can be installed and maintained by our team of highly experienced engineers.
A strong and reliable service is our mandate under HF Plumbing/Heating and AC. We invest heavily in the training and development of our team to ensure that all commercial and domestic plumbing, heating and air conditioning services are carried out to the standards expected under the HF name.
From industrial heating to plumbing systems, air conditioning installation and servicing to domestic plumbing/heating issues, HF Group specialise in all commercial, retail and domestic plumbing, heating and air conditioning services. It is why our customers come back to us again and again.
If you would like to know more about our Plumbing, Heating & Air Conditioning Services, examples of the work we have done in this sector or if you have any questions about bespoke services that you are looking for, please call our head office in Glasgow on 0800 783 9480 or email info@hf-group.co.uk. We look forward to hearing from you soon.


text:
[A51] Query - Use of Kraken with CPUs
Joel Eriksson joel.eriksson at gmail.com
Wed Mar 26 17:58:21 CET 2014
Previous message: [A51] Query - Use of Kraken with CPUs
Next message: [A51] Query - Use of Kraken with CPUs
Radeon GPUs were originally made by ATI. ATI was later acquired by AMD, but
the GPUs are certainly not AMD CPUs and the performance when it comes to
the kind of computations that are required for A5/1 and crypto in general
is not even close when you compare CPUs and GPUs. The reason for this is
mainly because in a single GPU, there are actually up to thousands of cores
that performs the actual computations. In the case of Radeon HD 6990, for
instance, you have 2 GPUs that have 1536 cores each, so 3072 cores in
total. Compare that to an ordinary CPU, and you realize that a multi core
CPU does not even come close. :)
So no, it's not about using the GPU to get some extra power instead of just
letting it sit idle. GPUs are way, way faster than CPUs for this kind of
stuff. For a bit more detailed information about why this is the case, I
advise you to read this:
https://en.bitcoin.it/wiki/Why_a_GPU_mines_faster_than_a_CPU
"A CPU core can execute *4* 32-bit instructions per clock (using a 128-bit
SSE instruction) or *8* via AVX (256-Bit), whereas a GPU like the Radeon HD
5970 can execute *3200* 32-bit instructions per clock (using its 3200 ALUs
or shaders). This is a difference of *800 (or 400 in case of AVX) times
more instructions per clock*."
Specifically, AMD/ATI GPUs are the best suited for these kinds of
computations, which is why they are used rather than NVidia based cards.
This is because AMD/ATI cards (once again, GPUs, not CPUs ;) have a number
of features that make them well suitable for high performing integer
operations. Traditionally, GPUs are better suited for floating point
operations because that is more important for gaming/graphics performance
in general. If we take Bitcoin mining (i.e SHA-256 computations) as an
example, the Radeon HD 7970 is about five times as fast as the GTX 680.
Joel Eriksson
clevcode.org
On Wed, Mar 26, 2014 at 5:39 PM, Nikos Balkanas <nbalkanas at gmail.com> wrote:
> On Wed, Mar 26, 2014 at 5:12 PM, Joel Eriksson <joel.eriksson at gmail.com>wrote:
>> Using CPUs instead of GPUs doesn't make any sense at all, CPUs are a
>> _lot_ slower than GPUs for these kinds of computations and you would need a
>> cluster (i.e much more expensive) to be able to get similar performance.
> You don't need a cluster for a multiprocessing board. Just a
> multiprocessing kernel that linux provides. Radeon's GPUs are, to my
> knowledge, AMD CPUs, but at lower frequencies. Granted, you don't have a
> general kernel running on top of them, but an MP kernel has load balancing
> and preemptive multitasking that kraken hasn't. ;-)
> But we are in agreement here. If you have a GPU sitting idle, why not take
> advantage of it?
> To really crush both CPUs and GPUs, you could create an ASIC for it
>> instead. I bet that there are A5/1 cracking ASICs out there already, just
>> not in the hands of the public AFAIK. Using FPGAs would be a decent middle
>> ground.
> Yeap.
>> Joel
>> On Wed, Mar 26, 2014 at 2:22 PM, Nikos Balkanas <nbalkanas at gmail.com>wrote:
>>> On Wed, Mar 26, 2014 at 1:51 PM, Joel Eriksson <joel.eriksson at gmail.com>wrote:
>>>> It will be _a lot_ slower. If you want to have any chance of
>>>> intercepting frequency hopping calls (without having receivers constantly
>>>> recording everything at each of the possible frequencies) you need to use
>>>> GPUs and SSDs. If you don't have to deal with frequency hopping, and don't
>>>> have to decipher in near real-time, it doesn't matter as much.
>>>> Joel
>>> In such case, wouldn't it make more sense to have more CPUs on the MB?
>>>> On Wed, Mar 26, 2014 at 11:36 AM, Nikos Balkanas <nbalkanas at gmail.com>wrote:
>>>>> On Wed, Mar 26, 2014 at 8:40 AM, Amber and Sarosh <
>>>>> amber_sarosh at hotmail.com> wrote:
>>>>>> Hi All,
>>>>>> Can anyone please guide if GPUs are necessary for rainbow table
>>>>>> lookup using kraken to find the key to decipher an intercepted
>>>>>> communication or is it possible to do this using just CPUs? In case the
>>>>>> later is possible how much time it will take approximately?
>>>>> GPUs are not necessary, just desirable. If GPUs are missing, kraken
>>>>> will still work with A5Cpu.so, but it will be somewhat slower. Assuming
>>>>> that during cracking your PC is CPU limited, the benefit should scale
>>>>> roughly with your setup ratio of GPU power/CPU power. In reality you will
>>>>> run into RAM and table I/O bottlenecks before that. In short it is highly
>>>>> depended on your setup ;-)
>>>>> The idea is, that the easier factor to improve is the CPU, so why not
>>>>> do it?
>>>>> Nikos
>>>>>> Naheed, Amber & Sarosh
>>>>>> A51 mailing list
>>>>>> A51 at lists.srlabs.de
>>>>>> https://lists.srlabs.de/cgi-bin/mailman/listinfo/a51
>>>>> A51 mailing list
>>>>> A51 at lists.srlabs.de
>>>>> https://lists.srlabs.de/cgi-bin/mailman/listinfo/a51
>>>> Best Regards,
>>>>   Joel Eriksson
>> Best Regards,
>>   Joel Eriksson
URL: <http://lists.srlabs.de/pipermail/a51/attachments/20140326/3ad1745c/attachment.html>


As government and the insurance industry continue their quest to control health care, your clinical autonomy is in jeopardy. Now more than ever, you need to fight and advocate to keep medical decisions in your well-trained hands.
Fortunately, you do not have to wage the fight alone. Successful legislative advocacy depends upon an integrated approach, consisting of lobbying, grassroots activity and political action through the California Medical Association's (CMA) California Medical Association Political Action Committee (CALPAC).
Operated by physicians for physicians, CALPAC supports hundreds of candidates for state and federal office who share CMA's philosophy and vision of the future of health care and medical practice.
Strengthen your political voice and protect the practice of medicine.
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Contributions made in error may be refunded within thirty (30) days by contacting CALPAC at (800)CALPAC-9.


VoteHere, a maker of security software for voting machines, publishes the source code for its product online in hopes that peer review will reveal any weaknesses.
VoteHere, a maker of security software for voting machines, published the source code for its product online in hopes of garnering additional analysis of its method for verifying the integrity of electronic votes.
The move comes as questions arise about the security of electronic and Internet voting.
Though on March 1, Super Tuesday, have .
Some states, Michigan among them, are going full bore to ballots cast on the Internet, despite some computer scientists' concerns that the Net is not secure enough to prevent election tampering. About 28 percent of Michigan voters cast their ballot online in February during that state's Democratic caucus. In the same month, the Department of Defense backed away from plans to conduct a trial that could have let the 6 million Americans abroad cast their vote online.
VoteHere has had its own security issues to deal with as well. In December, the company called in the FBI to . Adler said the investigation was ongoing and stressed that VoteHere's plans to release source code had been in the works since last summer.


If I look back and see my travels, exploration in 2015, I would be bit disappointed at myself. Whatever the reasons are, I couldn't travel much. Now in 2016 I have to cover up and explore places as much as I can.
Year 2016 started with traveling to Talakadu village. Initially My plan was to explore Hassan and Shravanabelagola but last minute change leads me to Talakadu. Another unexplored, lesser known place but architectural wonder and with great history. Talakadu once a magnificent city with more than 36 temples but sadly this city was buried under sand in 16th century.
Talakadu village is at the banks of Cauvery river. We visited river side first. Place was crowded, children playing, coracle ride available, street foods. it was kind of perfect family destination.
A curse has believed to be casted on the Wadiyar in 1612 by Alamelamma, wife of King Tirumalaraja, who ruled the Vijayanagar Empire. Wadiyar the ruling dynasty of Mysore were waiting for an opportune moment to overthrow the Vijayanagara dynasty. When King Tirumalaraja, died due to illness, Alamelamma – the second queen in the palace took over the administraion. Wadiyar seized this opportunity and annexed Srirangapatnam. Wadiya demanded Alamelamma to handover all the priceless jewels which she used to adorn the deity at Sri Ranganathaswamy temple in Srirangapatnam. The queen refused to give and when she got opportunity she escaped and reached Talakadu. Wadiyar sent soldiers after him and when queen Alamelamma saw them coming, she ran over to a cliff overlooking the Kaveri river, curse before jumping to death.
Soon after her curse Talakadu village and 36 temples were buried under mile deep sand. Now only 6 temples can be seen, excavated by ASI, remaining 30 Temples and palace still buried under sand. Also the alternate generations of Wadiyars continued to have no children, thereby no heirs to the dynasty, forcing them to adopt.
The name Talakadu is the combination of Twin brothers-Rulers by name 'Tala' and 'Kādu'= 'Talakadu'. There are two stone images of those brothers in front of Lord Veerabadraswamy temple here.
We hired one guide there, who talked about the entire story, the curse, eexplained about the history and architecture of all the temples. After Vaidyaswara temple, we headed to another temple nearby and our guide told us story of Tala and Kada, the two hunters, after whom this town in named. You can see their idol at the door of this temple.
Now there is another theory that explain the Talakadu story about the sand dunes. This is because of an ecological disaster stemming from the construction of a dam in 1336 by Madhav Mantri a minister of the Vijayanagar Empire. This dam caused the sand on the river bed to be exposed to the strong winds that are frequent in Talakadu. Not sure which one is true, story remains unresolved.


text:
Former Georgia All-American Bacarri Rambo arrested for alleged rape
Bacarri Jamon Rambo
Former Georgia All-American football player Bacarri Jamon Rambo was arrested on a rape charge Monday night, according to the Athens-Clarke County Police Department.
Rambo, 29, played for the University of Georgia Bulldogs from 2009 through 2012.
"On June 13, 2020, the ACCPD began an investigation into the rape of a 21-year-old female UGA student, which occurred at a downtown residence," police stated in a Tuesday morning media release. Rambo was booked into the Clarke County Jail on the warrant at about 10 p.m. Monday.
Bail had not been set as of late Tuesday morning.
According to a police incident report, the alleged rape was reported at 1:17 a.m. Saturday.
The report listed the "location of occurrence" as Georgia Height Apartments at 150 W. Broad St., the same address under which Rambo was booked into jail.
The victim reportedly identified Rambo as her attacker from the former football player's Instagram profile.
Rambo shares Georgia's all-time interceptions record of 16.
He was named a first-team All-American following his junior season in 2011.
The former safety was a sixth-round NFL draft pick of the Washington Redskins in 2013, spending two seasons with that franchise before moving on to Buffalo.
Rambo spent the 2014 and 2015 seasons with the Bills before going to Miami in 2016. He was cut by Buffalo in the 2017 preseason, ending his NFL career.
Rambo returned to UGA in 2018 when head coach Kirby Smart brought him onto his staff as an intern.
Anyone who has been sexually assaulted or knows someone who has can contact The Cottage Sexual Assault Center and Children's Advocacy Center. The agency provides a range of free services to child and adult victims of sexual and physical abuse, including medical care, advocacy, referrals, counseling and support groups. The Cottage also maintains a 24-hour crisis and information hotline at (877) 363-1912. For more information visit www.northgeorgiacottage.org


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Q: Passing CSS Values Through JavaScript to Partial View I am working with an MVC Entity Framework Webapp. I have a view that displays other partial views that are updated every 30 seconds. The issue is the dynamic progress bar I am using does not fill up at all and I have tried everything I know. The problem I think is the css that gets passed to the partial view ("width", current_progress + "%"). Here is a pic and the bar is supposed to be over half full...

Controller methods:
    public ActionResult Dashboard()
    {
        ViewBag.SumofDon = db.tblDonors.Sum(s => s.DonationAmount);
        return View(db.tblDonors.ToList());
    }

    public ActionResult Progress()
    {
        return PartialView("_Progress", db.tblDonors.ToList());
    }

Dashboard.cshtml:
@model IEnumerable<bssp.Models.tblDonor>

@{
    ViewBag.Title = "Dashboard";
}

@section Scripts{

}

        @Html.Partial("_Progress")

Partial view:
@model IEnumerable<bssp.Models.tblDonor>

@String.Format("{0:C}", @ViewBag.SumofDon) out of $20,000

 @*The width is what gets updated because it found the id of dynamic*@

Any help would be awesome and thanks in advance!

A: I think your issue is that you pull in the html from the partial with a style="width: 0%" but then jQuery that adjusts the css, $("#dynamic").css("width", current_progress + "%"), is only run on page load, not after the partial reloads.  You have two options to fix this,

*

*Run the jQuery function after the razor loads in from the partial, in the success method of the ajax.

*Since you are using razor to create the partial, why not just do the calculation right there?  That way the partial comes in already set up with the width set.  This is the easier and faster option of the two.


The President of ICMSA met EU Agriculture Commissioner, Mr. Phil Hogan, today in Brussels to discuss the ongoing uncertainty over Brexit and the crippling effect the chaos is having on Ireland's farming and wider agri-food sector and the financial losses being suffered by farmers.
Pat McCormack said that the whole sector had been in a state of 'suspended amination' for going on three years since the Referendum had put a massive question mark over our traditional markets in Britain but he was categorical that it is the primary producer – the farmer – who is taking the financial hit.
"We have been unable to make the kinds of decisions that are urgently required for a forward-planning business like farming because we just don't know whether our multi-billion British market for beef and dairy is going to be feasible the other side of Brexit", said Mr McCormack.
"There is a consensus now that confidence has effectively collapsed in beef and ICMSA has no doubt whatsoever that the losses suffered do come under the heading of Brexit. This is why farmer anger is growing given the complete lack of support to-date and the fact that Brexit is already damaging Irish farming", he said.
The ICMSA President said that he had asked Commissioner Hogan to accept that fact and act immediately to publish the supports that will be available to EU farmers already suffering demonstrable Brexit-related losses.
"We're well past the question of whether or not Brexit will cost Irish farmers money; it already has cost us money – and is continuing to do so every day". The EU Commission and our Government need to immediately set out their supports to restore a level of confidence amongst farmers regarding their futures, concluded Mr McCormack.


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Draghi: LTROs taking time to get into economy
The head of the European Central Bank Mario Draghi has told members of the European Parliament that liquidity actions had not gone into the economy fast enough.
Speaking to the European Parliament's Committee for Economic Affairs, Draghi said that the two long-term refinancing operations (LTROs) in December and February had yet to yield greater lending activity and that the process would take some time - available data suggesting that banks were parking the money on deposit to the central bank.
He commented: "We had hoped the LTRO money would go faster into the real economy. We are confident that central bank liquidity has come very close to the real economy. Of course, this does not mean that this will by itself boost lending to firms and households."
However, he added that it was encouraging that a very large number of small banks had participated in the LTROs.
"Small banks are best placed to refinance the real economy, in particular small- and medium-sized firms which are the biggest generator of employment in the economy," he said.
The ECB's quarterly survey on bank lending found that a tightening of credit conditions had declined substantially in the first three months of the year with banks expecting the trend to continue into the second quarter.
Draghi said the results were "positive" and added that the impact of the sovereign dent crisis on funding conditions had decreased, although the effects were still to be felt.
He continued: "The LTROs have been quite timely and all in all successful and if the only thing we managed was to buy time, then that is an extraordinary success. Buying time is not a minor achievement."
Holding out for a debt restructure
Greece stands before a default abyss but, as Simon Miller discovers, before it rushes to restructure, there are litigating risks from international trade treaties to consider
CFTC chief calls for observable transaction rate


Systematic mesh and nodal descriptions of the laws of statics and kinematics for the limiting state of plastic collapse in a structural system are set out. Then the constitutive relations appropriate to this condition are presented in such a way as to emphasise their inherent complementarity. The mixing together of these three independent ingredients — statics, kinematics and material constitution — gives rise to the vectorial formulation which governs plastic collapse: it is identified as a linear complementarity problem. From it are derived the dual linear programs which give expression to the variational principles associated with upper and lower bounds on the collapse load factor.


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Home Ronaldo How Many World Cup Goals Does Ronaldo Have?
How Many World Cup Goals Does Ronaldo Have?
He has scored a record 14 goals at the European Championships, seven at the World Cup finals, five in the UEFA Nations League and two at the Confederations Cup.
1 Who has more World Cup goals Ronaldo or Messi?
2 How many goals does Messi have in the World Cup?
3 Who holds the record for most goals in a single World Cup?
5 Who is faster Messi or Ronaldo?
7 Which goalkeeper has Messi scored against the most?
8 What is Rivaldo real name?
9 Who is the youngest World Cup winner?
10 Who is the only player who won the World Cup 3 times?
Who has more World Cup goals Ronaldo or Messi?
Messi has six goals at the FIFA World Cup, whereas, Ronaldo has bagged seven. Messi has 34 goals in friendlies as Ronaldo has scored 19.
How many goals does Messi have in the World Cup?
Messi has scored six times in FIFA World Cup tournaments: once in 2006, four times in 2014, when he guided his team to the final and was awarded the Golden Ball, and once in 2018. The remainder of Messi's goals, 34, have come in friendlies.
Who holds the record for most goals in a single World Cup?
Fontaine holds the record for the most goals scored at a single tournament, with 13 goals in 1958. The players that came closest were Kocsis in 1954, Müller in 1970 and Portugal's Eusébio in 1966, with 11, 10 and 9, respectively. The lowest scoring top scorer was in 1962, when six players tied at only four goals each.
You might be interested: FAQ: What Makes Ronaldo So Good?
Who is faster Messi or Ronaldo?
Which goalkeeper has Messi scored against the most?
Former Valencia goalkeeper Diego Alves has received 19 bottles as he is the goal-keeper Messi has scored the most goals against. Real Madrid goalkeeper Iker Casillas is next on the list and he has received 17 bottles. Earlier this week, Messi had posted an emotional message after the record-breaking goal.
What is Rivaldo real name?
Ali Daei of Iran was the first player to reach 100 goals in international football, having scored 109 in his career.
Who is the youngest World Cup winner?
The Final saw many records made in World Cup history that still stand as of 2018. At age 17, Pelé simultaneously became the youngest player to participate in, score, and win a World Cup final.
You might be interested: Quick Answer: How Many Awards Has Cristiano Ronaldo Won?
Who is the only player who won the World Cup 3 times?
Born Edson Arantes do Nascimento, the man who would come to be known as Pelé, burst onto the world soccer scene at age 16, excelling both for club team Santos and the Brazilian national side. By the end of his career, Pelé had won three FIFA World Cups with Brazil, the most wins of the World Cup by any player.
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